If I understand correctly, you are just using the barrel adjuster? Forgive if I just repeat stuff, but here goes:
(If the cables are all seated and capped correctly), shift into large front, small rear. Loosen the cable at the rear derailleur. Lightly force the derailleur arm inward while rotating the pedals till you reach 6th gear. Hold that position and tighten the "H" adjustment screw till it just stops. Let go of the derailleur. While rotating the pedals, back out the "H" screw till you just reach 7th gear; back a quarter turn more and this establishes a fool-proof chain limit. Pull the derailleur cable lightly tight and secure with the derailleur nut.
Shift into smallest front and rear second gear. Tighten the "L" screw till it just stops. While rotating the pedals, back out the "L" screw till you get 1st gear. Then back a quarter turn more and the upper chain limit should be golden.
Go through the shifts and use the Barrel Adjuster as necessary.
Hope that helps....